Cornerstone (statistics software)

Cornerstone (statistics software)

Original author(s)	BBN Technologies
Developer(s)	camLine GmbH
Initial release	1991 (1991)
Stable release	7.0
Development status	Active
Written in	C++
Operating system	Windows 7,Windows 10
Type	Statistics Software
License	proprietary
Website	www.camline.com/en/products/cornerstone.html

Cornerstone is a proprietary statistics software of the independent software vendor camLine GmbH. The software has a long tradition reaching back to the year 1991. Since then the owners of the software product have changed several times and since 2010 it is owned and maintained by camLine.

The application software primarily is designed for engineers in research and development or in manufacturing who need a tool for applied statistics. Cornerstone has a special focus on the fields of Analyses by Regression, Exploratory Data Analysis (EDA), quality control (control charts, process capability), and Design of Experiments (DoE).

Analyses are presented and recorded graphically in the form of a calculation graph (the so-called Workmaps). The structures can be saved in conjunction with the data and thus are reusable with similar data to perform the same analyses with refreshed or new data in the same structure. The software interactively combines all created objects in a logical execution sequence (live linking). That allows to actively connect the results and affect selections in all corresponding visualizations. In addition, changes in data get propagated to all dependent analyses and graphics.

Cornerstone is available in a 32-bit and as a 64-bit version. The later is capable of dealing with very large data sets above the 4GB limit which is known to be a typical restriction of the older 32-bit architecture. Otherwise the functionalities are identical. Until Cornerstone 7.0 the 64-bit version was named Cornerstone++. With version 7.0 the ++ extension is deprecated and the 64-bit version is the default and simply named Cornerstone. Starting with that release both versions are shipped and the user can decide which version to install.

History

Cornerstone version 1.0 was developed by BBN Software Products^[1] (since 1995 BBN Domain Corporation^[2] or rather Domain Manufacturing Corporation^[3]) as a follower to RS/1 since 1991. In 1999 Brooks Automation took^[4] over Domain Manufacturing^[5] including the Cornerstone software. The software business unit (including Cornerstone) of Brooks Automation^[5] was transferred to Applied Materials^[6] in 2007. camLine acquired the Cornerstone software in 2010^[7] and continues the development since then.

The original main feature in Cornerstone was Exploratory Data Analysis (EDA). EDA is an approach to analyzing data with visual methods to identify the main characteristics. It is used for seeing what the data can tell beyond formal modeling. Afterwards Cornerstone was expanded with additional key features. Design of Experiments (DoE) is used to figure out a small subset of experiments within all possibilities that provide initially defined questions. Linear regression models are used as analysis and optimization modeling technique.

Initially Cornerstone was available for UNIX based systems (SunOs, HP-UX) only. Since its version 1.5 introduced in March 1995 Microsoft Windows is supported too. camLine extended the DoE support and the analysis of large data sets above the 4GB limit. Due to the fact of low demand, the maintenance of UNIX based systems was discontinued in 2009 with version 5.0. The table below shows the history of versions of Cornerstone. The supported platforms as well as the publication date and the main innovations are listed.

Versions

Application and Availability

Cornerstone is applied in an industrial environment to analyze manufacturing and process data. The software is leveraged in Research and Development (R&D) to design experiments and analyze the results. This results currently in a focus on semiconductor and automotive sector. Anyhow users are found in other industrial areas with similar analysis tasks like photovoltaics, chemistry, paper, paint, optics, pharmaceutics, electronics and white goods. In addition Cornerstone is applied in industry-oriented academic sectors.

Recently, the capability of Cornerstone to analyze data efficiently is used more and more directly in the manufacturing environment. Most use cases deal with Cornerstone to condense the high amount of production data in cyclic analysis. The results are reported automatically on the intranet, for instance. In this application, a workmap is seen as an analysis template. Application engineers can develop these templates on the basis of well established workmaps. Therefore, it is possible to choose an individual and intuitive analysis depth. Improvements can be implemented and tested separately from the manufacturing process to ensure a reliable continued optimization.

Cornerstone is distributed by the software manufacturer, directly.

Scope of Operation

Essentially, all models are wrong, but some are useful.^[9]

Cornerstone is a statistical software^[10] which provides the essential analysis functions for engineers and natural scientists in a few modules. For instance, the analysis of variance and group comparisons are summarized within the regression module. This lean approach in Cornerstone supports engineers in doing appropriate statistical analysis.

Design of Experiments (DoE)

Design of Experiments(DoE) is used by engineers or applied scientist in physical or simulated experiments to reduce the number of runs. Each experiment is defined by a number of factors, for instance the oven temperature or the heating time. One run is defined by specific values of each factor. Hence, we have a huge number of runs which increase exponentially with the number of factors. The main question in DoE is to figure out a reliable small subset of runs to answer initially defined questions. These questions vary from the significance of a factor to predictions of unobserved areas in the experiment. Cornerstone focuses on D-optimal designs^[11] to select the subset of runs. They can be adjusted flexibly to practical requirements like constraints in the design space, integration of existing experiments, and model approaches in any order. The analysis of DoEs use regression methods for both categorical and continuous factors (incl. compositions). Cornerstone supports a standard evaluation procedure for regression analysis, which is described in.^[12][13]

In addition the following list outlines supported types of experimental designs in Cornerstone:

1. Full-factorial designs
2. Fractional-factorial designs
3. Plackett-Burman designs
4. Box-Behnken designs
5. Centrel-Composit designs
6. D-optimal designs
7. L9 / L18 / L28 / L36 as 3-level designs
8. Spacefilling designs
9. Optional User defined designs

2-field Taguchi designs are available for a robust parameter design. We recommend to replace them by D-optimal designs with a corresponding interaction structure.^[14] Mixture designs deal with the slack variable approach^[15] via D-optimal designs^[11] with constraint design space.

Exploratory Data Analysis (EDA)

Exploratory data analysis is detective work.^[16]

EDA is an approach to analyze data with visual methods to identify the main characteristics. It is used for seeing what the data can tell beyond formal modeling. In ^[17] Fahrmeir describes Exploratory Data Analysis as a method that goes further than descriptive statistics. It does not use stochastic and techniques based on probability theory but some of their methods are influenced by inductive statistics. Beyond the description and presentation of data, EDA is designed to identify structures and special characteristics in the data which often can lead to new questions or hypothesis in the corresponding application. According to Fahrmeir^[17] it is typically applied if the problem is not specified in detail or the choice of a suitable model is unclear yet.

Cornerstone includes graphical methods of EDA in combination with contemporary, continuous implemented interactive features like “brushing and linking”.^[18][19] These interactive techniques operate meaningfully across all linked objects in Cornerstone. For instance, if we highlight a date in a histogram (“brush”) the residuum belonging dataset from a regression is also highlighted in corresponding graphics. The datasets are connected comprehensively and are highlighted in all related objects, they are “linked” to. Its purpose is to reveal multivariate relations in small and especially in huge and complex datasets. For that matter Cornerstone goes with an exploratory rather than a confirmatory approach. Many parameters (resp. variables) can be analyzed by matrix graphics and the possibility to create many different graphic types in parallel. Statistical values and the corresponding confidence interval are listed or displayed wherever reasonable. All results in Cornerstone are available as tables and / or graphics. It is possible to export them in standard file types or via clipboard to arbitrary programs.

Regression

A regression analyses the relationship between dependent variables (response) and independent variables (factors, predictors). The linear regression provided in Cornerstone is the main tool of statistical analysis and uses quantitative and qualitative predictors. An evaluation of qualitative predictors is often done by an analysis of variance instead of a regression. The term “linear” relates to the power of the regression coefficients not the predictors. We describe the order of a regression model as the highest power of a predictor. Cornerstone is capable to fit models of arbitrary order.

The focus is on a compact and fast analysis of many responses versus many predictors (multiple multivariate regression) even if models of higher order are used. Missing values of a response influence only the corresponding regression.

A regression analysis provides statistical values of the linear models in tables. Graphical methods (Q-Q-Plot, Interaction Plot, different plots of residuals) are available within the regression module.

Selection of the power for a Box–Cox transformation of a response is done on the basis of a Box-Cox-Plot.^[20] The result of each regression analysis is a prediction with confidence intervals for each predictor with respect to each response. It is charted in an interactive prediction graph on the original (untransformed) scale for an optimal usage of the statistical model.

Multivariate Statistics

General linear models (regression), principal component analysis (PCA), and multivariate analysis of variance (MANOVA) are supported. The key aspect is on regression methods which summarize analysis of variance methods. It is described in section Regression and capable of analyzing many responses versus many predictors efficiently. A MANOVA provides the ability to determine whether two or more groups are different based on their relationship with multiple continuous responses. The well-known iris dataset by Anderson wants to evaluate the difference between three iris flower species related to their sepal and petal length and width. The MANOVA, which utilize a PCA, reveal the rules to classify a new flower with respect to its measurements. Furthermore, a PCA can be leveraged, for instance, to reduce the number of variables in a correlated dataset with the ability to control the loss of information.

Quality Methods

The software is capable of process capability analysis and control charts analysis for well established distribution types. A process capability analysis describes a process matching to predefined specification limits. The match is measured by different Cp indices and illustrated by a histogram with an overlay of the used distribution. Control charts are used to analyze manufacturing data off-line. It has the goals to identify unexpected variability and optimize the corresponding process afterwards. Utilizing two different rule sets, control charts provide a tool to determine unforeseen variation or changes in a process from the variability inherited by the process itself. Occasionally, sample size determination is used in this range which is dedicated to the DoE module.

Programming in Cornerstone Extension Language (CEL)

CEL is used to develop Cornerstone supplements and automate analysis work-flows. For instance, you can automate the preparation of a loaded dataset and its following analysis. Hence, CEL provides the possibility to develop additional work-flows inside Cornerstone which are tailored to your needs.

The internal class library is exposed and accessible via an adapted C++ development environment. It contains classes for nearly every object (e. g. dataset, regression, xyscatterplot) and its methods. The DoE module is not accessible via CEL. Functions in CEL can be triggered by notify events, like the startup, a reread of a dataset, or when dragging a reference line. This possibility is utilized when acting with Cornerstone externally.

See also

• Comparison of statistical packages
• Data mining
• Data processing
• Online analytical processing (OLAP)
• SQL

References

1. ↑ "Timeline of BBN Technologies". Raytheon BBN Technologies. Retrieved 2017-04-21.  zeitlicher Abriss über das Unternehmen seit 1948
2. ↑ "BBN Domain Corporation: A new name and a new focus; BBN subsidiary offers process optimization solutions to enable industrial companies to streamline operations and improve product development.". The Free Library. Farlex, Inc., USA. Retrieved 2017-04-21. 
3. ↑ "Domain Will OEM FASTech's STATIONworks Suite of Equipment Automation Solution Components". Brooks Automation, Inc., USA. 1998-07-15. Retrieved 2017-04-21.  Press release about the usage of Cornerstone as Domain Solution
4. ↑ "Brooks Automation to Acquire Domain Manufacturing". Brooks Automation, Inc., USA. 1999-06-23. Retrieved 2017-04-21.  Press release about ownership transition to Brooks and the usage of Cornerstone as Domain Solution
5. 1 2 "Brooks Automation". Brooks Automation, Inc., USA. Retrieved 2017-04-21.  Homepage of Brooks Automation
6. ↑ "Applied Materials Completes Acquisition of Brooks Software". Applied Materials, Inc., USA. 2007-03-30. Retrieved 2017-04-21.  Newsroom on the Homepage of Applied Materials
7. ↑ camLine GmbH (2011-08-25). "camLine launches Cornerstone Release 5.1". PresseBox - unn UNITED NEWS NETWORK GmbH. Retrieved 2017-04-21. 
8. 1 2 "Domain Announces Cornerstone 2.4 for UNIX, Windows 95 and Windows NT". Brooks Automation, Inc., USA. 1998-01-12. Retrieved 2017-04-21.  press release about the availability of Cornerstone version 2.4 by Brooks Automation
9. ↑ Box, G. E. P., and Draper, N. R.: Empirical Model Building and Response Surfaces, 1987, S. 424
10. ↑ Kleppmann: Versuchsplanung, 2011, Besprechung von Software für Versuchsplanung ab S. 278
11. 1 2 Peter Goos, Bradley Jones: Optimal Design of Experiments: A Case Study Approach, 2011, S. 34
12. ↑ Draper and Smith: Applied Regression Analysis, 1998, S. 335ff and 339ff
13. ↑ Fox: Applied Regression Analysis and Generalized Linear Models, 2008, S. 324
14. ↑ Hinkelmann and Kempthorne: Design and Analysis of Experiments, Volume 2, 2005, S. 636f
15. ↑ Cornell: A Primer on Experiments with Mixtures, 2011, S. 229
16. ↑ John W. Tukey: Exploratory Data Analysis. Addison and Wesley, 1977, Beginning of the book, ISBN 0201076160
17. 1 2 L. Fahrmeir, R. Künstler, I. Pigeot, G. Tutz: Statistik. Der Weg zur Datenanalyse., Springer, 1997, Seite 12., ISBN 978-3642019388
18. ↑ Richard A. Becker, William S. Cleveland and Allan R. Wilks: Dynamic Graphics for Data Analysis, Statistical Science, Vol. 2, No. 4 (Nov., 1987), pp. 355-383
19. ↑ Robert Voigt: An Extended Scatterplot Matrix and Case Studies in Information Visualization, Master's thesis, Hochschule Magdeburg-Stendal, 2002, Seite 10
20. ↑ Box, G. E. P., and Cox, D. R.: An Analysis of Transformations, Journal of the Royal Statistical Society Series B, Vol. 26, No. 2, 1964, S. 211-252

Literature

• Box, George E. P., and Draper, Norman R.: Empirical Model Building and Response Surfaces. Wiley 1987, New York, NY, ISBN 978-0471810339
• John A. Cornell: A Primer on Experiments with Mixtures. Wiley 2011, ISBN 978-0-470-64338-9
• Norman Draper & Harry Smith: Applied Regression Analysis, 3rd Edition. Wiley 1998, ISBN 978-0471170822
• John Fox: Applied Regression Analysis and Generalized Linear Models. Sage Publications 2008, ISBN 978-0761930426
• Peter Goos, Bradley Jones: Optimal Design of Experiments: A Case Study Approach. Wiley 2011, ISBN 978-0-470-74461-1
• Hinkelmann, K., and Kempthorne, O: Design and Analysis of Experiments. Volume 2, „Advanced Experimental Design". Wiley 2005, ISBN 978-0471551775
• Wilhelm Kleppmann: Versuchsplanung. Produkte und Prozesse optimieren. 7. aktualisierte und erweiterte Auflage, „Praxisreihe Qualitätswissen", Hanser München u. a. 2011, ISBN 978-3-446-42774-7

External links

• Applied Materials, Inc. - Homepage of Applied Materials, Inc.
• Brooks Automation, Inc. - Homepage of Brooks Automation, Inc.
• Raytheon BBN Technologies - Homepage of Raytheon BBN Technologies